Mean Log Jump Factor
Key Mean Log Jump Factor in Bates Model refers to the value of the parameter ν in the distribution of log(1+J) given by: log(1+J) ~ N(ν,δ²)
It equals the mean of the logarithm of the "jump factor" S'/S = 1+J in the underlying price poisson process, where S' is the underlying price right after a jump.
Note that due to the negative convexity of the log function, setting Ξ½ = 0 is actually equivalent to having mean(J) slightly greater than 0, leading to a positive average jump size.
This convexity effect is more pronounced when the variance of the jump size increases and vanishes when that variance also vanishes.
Therefore in order to remove the effect of jumps, provided a non-zero jump intensity, you must set simultaneously Mean Log Jump Factor = 0 and Vol Log Jump Factor = 0
Setting Mean Log Jump Factor < 0 means having predominantly negative jumps.
Contrary to initial intuition, this does not lead to lower call values, because the drift of the underlying price diffusion (i.e. the continuous part of the stochastic process) must then increase so that the total risk-neutral drift remains unchanged.